arXiv subjects

Hessa Al-Thani

Publications and source records attributed to Hessa Al-Thani.

5 recordsLinked to original sources

arXiv2025

Identifying Approximate Minimizers under Stochastic Uncertainty

We study a fundamental stochastic selection problem involving $n$ independent random variables, each of which can be queried at some cost. Given a tolerance level $δ$, the goal is to find a value that is $δ$-approximately minimum (or maximum) over all the random variables, at minimum expected cost. A solution to this problem is an adaptive sequence of queries, where the choice of the next query may depend on previously-observed values. Two variants arise, depending on whether the goal is to find a $δ$-minimum value or a $δ$-minimizer. When all query costs are uniform, we provide a $4$-approximation algorithm for both variants. When query costs are non-uniform, we provide a $5.83$-approximation algorithm for the $δ$-minimum value and a $7.47$-approximation for the $δ$-minimizer. All our algorithms rely on non-adaptive policies (that perform a fixed sequence of queries), so we also upper bound the corresponding ''adaptivity'' gaps. Our analysis relates the stopping probabilities in the algorithm and optimal policies, where a key step is in proving and using certain stochastic dominance properties.

cs.DS↗

arXiv2024

Minimum Cost Adaptive Submodular Cover

Adaptive submodularity is a fundamental concept in stochastic optimization, with numerous applications such as sensor placement, hypothesis identification and viral marketing. We consider the problem of minimum cost cover of adaptive-submodular functions, and provide a $4(1+\ln Q)$-approximation algorithm, where $Q$ is the goal value. In fact, we consider a significantly more general objective of minimizing the $p^{th}$ moment of the coverage cost, and show that our algorithm simultaneously achieves a $(p+1)^{p+1}\cdot (\ln Q+1)^p$ approximation guarantee for all $p\ge 1$. All our approximation ratios are best possible up to constant factors (assuming $P\ne NP$). Moreover, our results also extend to the setting where one wants to cover {\em multiple} adaptive-submodular functions. Finally, we evaluate the empirical performance of our algorithm on instances of hypothesis identification.

cs.DS↗

arXiv2023

Sparse Graphical Designs via Linear Programming

Graphical designs are a framework for sampling and numerical integration of functions on graphs. In this note, we introduce a method to address the trade-off between graphical design sparsity and accuracy. We show how to obtain sparse graphical designs via linear programming and design objective functions that aim to maximize their accuracy. We showcase our approach using yellow taxicab data from New York City.

math.OC↗

arXiv2023

Tridiagonal Maximum-Entropy Sampling and Tridiagonal Masks

The NP-hard maximum-entropy sampling problem (MESP) seeks a maximum (log-)determinant principal submatrix, of a given order, from an input covariance matrix $C$. We give an efficient dynamic-programming algorithm for MESP when $C$ (or its inverse) is tridiagonal and generalize it to the situation where the support graph of $C$ (or its inverse) is a spider graph with a constant number of legs (and beyond). We give a class of arrowhead covariance matrices $C$ for which a natural greedy algorithm solves MESP. A \emph{mask} $M$ for MESP is a correlation matrix with which we pre-process $C$, by taking the Hadamard product $M\circ C$. Upper bounds on MESP with $M\circ C$ give upper bounds on MESP with $C$. Most upper-bounding methods are much faster to apply, when the input matrix is tridiagonal, so we consider tridiagonal masks $M$ (which yield tridiagonal $M\circ C$). We make a detailed analysis of such tridiagonal masks, and develop a combinatorial local-search based upper-bounding method that takes advantage of fast computations on tridiagonal matrices.

math.OC↗

arXiv2020

An R Package for generating covariance matrices for maximum-entropy sampling from precipitation chemistry data

We present an open-source R package (MESgenCov v 0.1.0) for temporally fitting multivariate precipitation chemistry data and extracting a covariance matrix for use in the MESP (maximum-entropy sampling problem). We provide multiple functionalities for modeling and model assessment. The package is tightly coupled with NADP/NTN (National Atmospheric Deposition Program / National Trends Network) data from their set of 379 monitoring sites, 1978--present. The user specifies the sites, chemicals, and time period desired, fits an appropriate user-specified univariate model for each site and chemical selected, and the package produces a covariance matrix for use by MESP algorithms.

cs.MS↗